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I think all are possible: Reason being, to construct a triangle all that we need is a set of 3 distinct points and in this case we can bring 3 points as close as possible and also make it lie the circle (your imagination should work here).

i think the answer should 1, 2 and 3 are all possible..

hi fresinha, the radius of the circle is 1 units That means that the distance between the center of the circle and the vertices of the triangle is 1 i.e the radius .so when the internal distances are 1 how can the perimeter be <0

Which of the following can be a perimeter of a triangle inscribed in a circle of radius 1?

I. 0.001

II. 0.010

III. 0.100

I only III only II and III only I, II, and III not I, II, or III

As we can see, a triangle with 3 sides: a, b, c which is inscribed in a circle with the radius is 1. We assume a is the biggest side of the triangle. We have the perimeter = a + b + c > a + a = 2a Because the triangle is inscribled in a circle so a is always smaller than or equal to the diameter = 2. So, we have the perimeter > 2a >= 4. So E is the correct answer.

The point of giving the radius is just confusing the test takers. It doesn't matter at all. We have to place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle. Do you agree?
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The point of giving the radius is just confusing the test takers. It doesn't matter at all. We have to place all three vertices on a tiny arc of less than 0.001. The circle consists of infinite number of points. The circle isn't a straight line, so the three vertices will make a triangle. Do you agree?

boy this question did my head in today! nice tricky question and a great explanation. Can we update the explanation in the test with this one please. The OE in the test leaves a lot to be desired.

Even if it is not given the inscribed triangle is equilateral triangle , let's assume that the traingle is equilateral .

For an equilateral triangle inscribed in a circle side s = sqroot(3)*r ; with r =1 , side s = root(3) , so perimeter is 3*root(3) . Which is way off all the choices given in the question

intutively I think other triangle inscribed in the circle will have perimeter greater than equilateral triangle , but I don't have a good reasoning , I might be wrong . If some quant expert shed some light on this , would be great !

How did we come up with 0.001 ....why not 0.0001? What is the reasoning behind this lower bound? What is the logic behind 0.001 Does this have any connection with radius being =1?

How did we come up with 0.001 ....why not 0.0001? What is the reasoning behind this lower bound? What is the logic behind 0.001 Does this have any connection with radius being =1?

The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: P>0.

Equilateral triangle has the least perimeter. So, any triangle will have a perimeter greater than that of an equilateral triangle.

Also, radius of the circle= 1 unit This means, the distance from the center of the circle to the vertex of the triangle = 1 unit

we know that the value of the third side of a triangle lies between the sum and difference of the other two sides. Therefore, 0<a<2, 0< b<2, 0<c<2 => 0<a+b+c<6 so, the perimeter is greater than 0.